Question

a balloon filled with oxygen gas (o₂) has a volume of 4,558 cubic centimeters. squeezing the balloon causes the volume to decrease to 4,002 cubic centimeters and the internal pressure to increase to 935 torr. what was the initial pressure of the o₂ gas in the balloon before it was squeezed? assume ideal gas behavior and a constant temperature. write your answer to the correct number of significant figures. round if necessary. torr save answer

Explanation:

Step1: Recall Boyle's Law

Boyle's Law states that for an ideal gas at constant temperature, \( P_1V_1 = P_2V_2 \), where \( P_1 \) is the initial pressure, \( V_1 \) is the initial volume, \( P_2 \) is the final pressure, and \( V_2 \) is the final volume.

Step2: Identify known values

We know that \( V_1 = 4558 \, \text{cm}^3 \), \( V_2 = 4002 \, \text{cm}^3 \), and \( P_2 = 935 \, \text{torr} \). We need to find \( P_1 \).

Step3: Rearrange Boyle's Law to solve for \( P_1 \)

From \( P_1V_1 = P_2V_2 \), we can solve for \( P_1 \) by dividing both sides by \( V_1 \): \( P_1=\frac{P_2V_2}{V_1} \)

Step4: Substitute the known values into the formula

Substitute \( P_2 = 935 \, \text{torr} \), \( V_2 = 4002 \, \text{cm}^3 \), and \( V_1 = 4558 \, \text{cm}^3 \) into the formula:
\( P_1=\frac{935 \times 4002}{4558} \)
First, calculate the numerator: \( 935\times4002 = 935\times(4000 + 2)=935\times4000+935\times2 = 3740000+1870 = 3741870 \)
Then, divide by the denominator: \( \frac{3741870}{4558}\approx819 \) (rounded to the correct number of significant figures. The values \( 4558 \) (4 sig figs), \( 4002 \) (4 sig figs), and \( 935 \) (3 sig figs) – the least number of sig figs in the given values is 3, but our calculation gives approximately 819 which has 3 sig figs as well)

Answer:

819 torr